$9^{123456789} \pmod{100}$ , retrace calculation operation
Remember that $9=3^2$. From Euler's theorem we know that $3^{40}\equiv 1\pmod {100}$, so that $9^{20}\equiv 1\pmod{100}$.
Remember that $9=3^2$. From Euler's theorem we know that $3^{40}\equiv 1\pmod {100}$, so that $9^{20}\equiv 1\pmod{100}$.